As the title itself says, "Color of Water" is a tribute to a white mother from her black son, and a memoir citing the experiences of a child who aimed to find his place in society, and within his people. The theme of self-identity comes straight from the words of McBride as he confronted his brothers and his mother and would continuously ask whether he was adopted or not, simply because he and his mother did not look alike. The string of the "color of water" came from his mother as she said that water has no color, and we are equally "colorless". McBride's self of identity came as a result of the intervention of his mother, and her insistance that their family opted to not let color be a priority in their view of self or others, and that God loved all people equally.
Mechanically speaking, the theme of self-identity you could say is developed through dialogue, self-realization, exploration, and comparison throughout the novel as it is a memoir and autobiographical account of a specific situation.